JEE Main General questions with solutions

Q1. One mole of nitrogen gas at a pressure of 0.8 atm takes 38 s to effuse through a small pinhole. Under the same conditions but at a pressure of 1.6 atm, one mole of a xenon fluoride compound takes 57 s to effuse through the same hole. What is the molar mass (in g/mol) of the xenon fluoride compound?

1. 128
2. 196
3. 254
4. 320

Answer: 254

Using the modified Graham's law where effusion rate is proportional to P/sqrt(M), setting the rates equal for both gases gives the molar mass of the xenon fluoride as 254 g/mol, which corresponds to XeF4.

Q2. In the reaction below, identify reagent A: A benzyl ketone (PhCH2COCH3) reacts with reagent A in the presence of NaOH to give a beta-hydroxy ketone product via an aldol-type reaction. What is A?

1. CH3CHO
2. Ethylene oxide (oxirane)
3. CH3COOC2H5
4. HCHO

Answer: HCHO

In an aldol reaction with NaOH, the enolate of the ketone attacks the aldehyde carbonyl. Formaldehyde (HCHO) is a non-enolisable aldehyde that acts purely as the electrophilic carbonyl partner, giving a primary beta-hydroxy ketone. CH3CHO would also work but gives a secondary alcohol. The question specifies the product is the beta-hydroxy ketone formed from attack on HCHO, making the product PhCH2COCH2CH2OH or similar primary-alcohol adduct. HCHO is the correct reagent A.

Q3. Two identical spherical raindrops, each of radius r, fall through air at terminal velocity v cm/s. When the two drops coalesce into one larger drop, what is the terminal velocity of the combined drop?

1. 4 v
2. (4)^(1/3) v
3. 2 v
4. 64 v

Answer: (4)^(1/3) v

Volume conservation: (4/3)*pi*R³ = 2*(4/3)*pi*r³ => R = 2^(1/3) r. Since v_T proportional to r²: v' = v * (2^(1/3))² = v * 4^(1/3).